Can large fermion chemical potentials suppress the electroweak phase transition ?

We calculate the critical temperature $(T_c$) of the electroweak phase transition in the minimal standard model considering simultaneously temperature ($T$) and fermion chemical potential ($\mu_f$) effects over the effective potential. The calculation is performed in the one-loop approximation to the effective potential at non-zero temperature using the real time formalism of the thermal field theory. We show that it exists a fermion chemical potential critical value ($\mu_f^c$) for which the Higgs boson condensate vanishes at T=0. If $T$ and $\mu_f$ effects are considered simultaneously, it is shown that for $\mu_f \geq \mu_f^c$ then $T_c^2 \leq 0$, implying that the electroweak phase transition might not take place.